Finite Group Databasebeta

← Prev (#31775231) Next (#31775233) →

C5×D21×C83 #31775232

order17430
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C5×C83 · Schur multiplier (H2) = C1

Aliases

direct productC5×D21×C83
unambiguous semidirect productC3⋊(C5×D7×C83)
unambiguous semidirect productC7⋊(C5×D3×C83)

Splittings

Fitting, socle, HallC3×C5×C7×C83 ⋊ C2
derived, HallC3×C7 ⋊ C2×C5×C83
HallC5×C7×C83 ⋊ D3
HallC3×C7×C83 ⋊ C2×C5
HallC3×C5×C83 ⋊ D7
HallC7×C83 ⋊ C5×D3
HallC3×C83 ⋊ C5×D7
HallC3×C5×C7 ⋊ C2×C83
HallC5×C7 ⋊ D3×C83
HallC3×C5 ⋊ D7×C83
SylowC7 ⋊ C5×D3×C83
SylowC3 ⋊ C5×D7×C83

Subgroups

subgroupG/H
center, hypercenterC5×C83D21
commutator, cosocle, hypocenterC3×C7C2×C5×C83
FrattiniC1G
Fitting, socleC3×C5×C7×C83C2
LCSG ▷ C3×C7
UCSC1 ◁ C5×C83

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8715

Conjugacy classes & character table

4980 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D83, C5×D3×D7×C83, C5×D21⋊D83, …
maximal normal subgroup ofC5×D21×D83, C5×D3×D7×C83, C5×D21⋊D83, …
maximal quotient ofC5×C83×Dic21, C2×C5×D21×C83

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17430, 12);